向量优化的高阶微分条件

A Study of Higher Order Differential Conditions for Vector Optimization

研究Pareto有效解次微分形式判定法,讨论非光滑条件下Pareto解的存在性,建立从Rn到Rm上的Ck,1函数的高阶优化条件,然后应用高次微分形式的泰勒公式研究从Rn到Rm上的Ck,1函数的Pareto解的纯量形式最优性条件,并给出弱C-准凸和C-准凸函数的二阶判定条件,完成对Pareto解的充分条件的进一步研究.

In this paper,we study the discriminant method for Pareto effective solutions of sub differential form,discuss the existence of Pareto solutions under the condition of nonsmooth,and establish highorder optimality conditions for Ck,1 functions from Rn to Rm.Then we study the scalar form optimality conditions of Pareto solutions for Ck,1 functions from Rn to Rm using the Taylor formula of highorder differential form,and give the second order criteria for weak Cquasiconvex and Cquasiconvex functions in order to complete the further study of sufficient conditions for Pareto solutions.